| Discontinuous Galerkin (DG) methods are high-order accurate, compact-stencil methods, proven to possess favorable properties for highly efficient parallel systems, complex geometries and unstructured meshes. Coding effort is significantly reduced for compact-stencil DG methods in comparison to main stream finite difference and finite volume methods. This work successfully introduces DG methods to thermal ablation and non-equilibrium hypersonic flows.;In the state-of-the-art hypersonic flow codes, surface heating predictions are very sensitive to mesh resolution in the shock. A minor misalignment can cause major changes in the heating predictions. This is due to the lack of high-order accuracy in current streamline methods and numerical errors associated with the shock capturing approach. Shock capturing methods like slope limiter or artificial viscosity, being empirical have errors in the shock region.;This work employs r-p adaptivity to accurately capture the shock with p = 0 elements (first order accuracy). Smooth flow regions are captured using p greater than 0. This method is stable. Implicit methods are developed for solution advancement with high CFL numbers. Error in the shock is reduced by redistributing the elements (outside of the shock) to within the shock (r adaptivity). Inviscid and viscous hypersonic flow problems, with same accuracy as in h-p adaptivity method, are simulated with one-third elements. This methodology requires no a priori knowledge of the shock's location, and is suitable for detached shock problems.;r-p adaptivity method has allowed for successful prediction of surface heating rate for hypersonic flow over cylinder. Additionally, good comparisons are made, for non-equilibrium hypersonic flows, to the published results. This tool is also used to determine the effect of micro-second pulsed sinusoidal Dielectric Barrier Discharge (DBD) plasma actuators on the surface heating reduction for hypersonic flow over cylinder. A significant effect, of the plasma actuators, is found on the surface heating for hypersonic flows (with and without thermo-chemistry) and several designs are investigated for optimum heating reduction. |
